{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ceed6db0",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import math\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from sympy import symbols, cos, sin\n",
    "from sympy.plotting import plot_parametric\n",
    "from math import sin,cos\n",
    "import random"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e2d6e3c",
   "metadata": {},
   "source": [
    "# Лабораторная работа 1.4 - Фильтр Рао-Блэквулла\n",
    "Рассматривается приложение калмановской фильтрации к задаче определения ориентации абсолютно твердого тела на основе измерений, регистрируемых акселерометром и гироскопом. Реализован расширенный Фильтр Рао-Блэквулла, в рамках модели пространства состояний, изложенной в M. Kok, J. D. Hol and T. B. Schön (2017). Using Inertial Sensors for Position and Orientation Estimation. Foundations and Trends in Signal Processing: Vol. 11: No.\n",
    "1-2, pp 1-153. doi: 10.1561/2000000094"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "85922c72",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Начальные данные\n",
    "#период дискретизации\n",
    "T = 0.05\n",
    "t = []\n",
    "t.append(0)\n",
    "# вектор ускорения свободного падения\n",
    "g = np.array([0,0,9.81])\n",
    "#матрица шума ориентации\n",
    "w_n = np.array([[0.05,0.0,0.0],[0.0,0.05,0.0],[0.0,0.0,0.05]])\n",
    "# матрица шума измерения\n",
    "e_n = np.array([[0.1,0.0,0.0],[0.0,0.1,0.0],[0.0,0.0,0.1]])\n",
    "# вектор состояния\n",
    "q = np.array([0,1/3,1/3,1/3])\n",
    "m  = []\n",
    "P = []\n",
    "m.append(q)\n",
    "P.append(np.array([[0.1,0.0,0.0,0.0],[0.0,0.1,0.0,0.0],[0.0,0.0,0.1,0.0],[0.0,0.0,0.0,1.0]]))\n",
    "# угловая скорость\n",
    "w = np.array([0.5,0.5,0])\n",
    "# количество измерений\n",
    "N = 250\n",
    "Q = []\n",
    "X = []\n",
    "X.append(q)\n",
    "# Вектор наблюдений\n",
    "Y = []\n",
    "F_p = np.array([0.0,0.0,0.0])\n",
    "Y.append(q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a741bd0e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def Q(q):\n",
    "    return np.array([[2*q[0]**2-1+2*q[1]**2, 2*(q[1]*q[2]-q[0]*q[3]), 2*(q[1]*q[3]+q[0]*q[2])],\n",
    "[2*(q[1]*q[2]+q[0]*q[3]), 2*q[0]**2-1+2*q[2]**2, 2*(q[2]*q[3]-q[0]*q[1])],\n",
    "      [2*(q[1]*q[3]-q[0]*q[2]), 2*(q[2]*q[3]+q[0]*q[1]), 2*q[0]**2-1+2*q[3]**2]])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "3db053f8",
   "metadata": {},
   "outputs": [],
   "source": [
    "def Omega(w):\n",
    "    return np.array([[0, -w[0], -w[1], -w[2]],\n",
    "      [w[0],     0,  w[2], -w[1]],\n",
    "      [w[1], -w[2],    0,   w[0]],\n",
    "      [w[2],  w[1], -w[0],     0]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "34bc700d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def F_w(w):\n",
    "    return np.array([[1.0,0.0,0.0,0.0],[0.0,1.0,0.0,0.0],[0.0,0.0,1.0,0.0],[0.0,0.0,0.0,1.0]]) + 0.5 * Omega(w) * T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d93d3ff4",
   "metadata": {},
   "outputs": [],
   "source": [
    "def Xi(q):\n",
    "    return np.array([[\n",
    "      -q[1], -q[2], -q[3]],\n",
    "      [ q[0], -q[3],  q[2]],\n",
    "       [q[3],  q[0], -q[1]],\n",
    "      [-q[2],  q[1],  q[0]]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "55c32129",
   "metadata": {},
   "outputs": [],
   "source": [
    "def F_q(q):\n",
    "    return 0.5 * Xi(q)*T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3f022893",
   "metadata": {},
   "outputs": [],
   "source": [
    "def norm(q):\n",
    "    sgn = 0\n",
    "    if q[0] > 0 :\n",
    "        sgn = 1\n",
    "    if q[0] < 0 :\n",
    "        sgn = -1\n",
    "    l = math.sqrt(q[0]**2 + q[1]**2 + q[2]**2 + q[3]**2)\n",
    "    return sgn * q / l\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "dc66a3b7",
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(1,N):\n",
    "    t.append(i*T)\n",
    "    y = np.dot(Q(q).transpose(),np.array(g + F_p + np.random.multivariate_normal([0,0,0],e_n)))\n",
    "    q_ = np.dot(F_w(w),q)+ np.dot(F_q(q), np.random.multivariate_normal([0,0,0],w_n))\n",
    "    q = norm(q_)\n",
    "    X.append(q)\n",
    "    Y.append(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "8803aad7",
   "metadata": {},
   "outputs": [],
   "source": [
    "def H(q):\n",
    "    d_0 = np.array([\n",
    "         [4*q[0],  2*q[3], -2*q[2]],\n",
    "         [-2*q[3],  4*q[0],  2*q[1]],\n",
    "         [2*q[2], -2*q[1],  4*q[0]]])\n",
    "    d_1 = np.array([\n",
    "        [4*q[1],  2*q[2],  2*q[3]],\n",
    "        [2*q[2],       0,  2*q[0]],\n",
    "        [2*q[3], -2*q[0],       0]])\n",
    "    d_2 =np.array([ \n",
    "        [     0,  2*q[1], -2*q[0]],\n",
    "        [2*q[1],  4*q[2],  2*q[3]],\n",
    "        [2*q[0],  2*q[3],       0]])\n",
    "    d_3 = np.array([\n",
    "        [      0,  2*q[0],  2*q[1]],\n",
    "        [-2*q[0],       0,  2*q[2]],\n",
    "        [ 2*q[1],  2*q[2],  4*q[3]]])\n",
    "    t0 = np.dot(d_0,g)\n",
    "    t1 = np.dot(d_1,g)\n",
    "    t2 = np.dot(d_2,g)\n",
    "    t3 = np.dot(d_3,g)\n",
    "    ans  = np.array([[t0[0],t1[0],t2[0],t3[0]],[t0[1],t1[1],t2[1],t3[1]],[t0[2],t1[2],t2[2],t3[2]]])\n",
    "    return ans"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "d35569b1",
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(1,len(Y)):\n",
    "    # Прогноз\n",
    "    m_ = np.dot(F_w(w),m[-1])\n",
    "    p_ = np.dot(np.dot(F_w(w),P[-1]),(F_w(w)).transpose()) + np.dot(np.dot(F_q(m[-1]), w_n) , F_q(m[-1]).transpose())\n",
    "\n",
    "    # Коррекция\n",
    "    S = np.dot(np.dot(H(m_),p_),H(m_).transpose())+ w_n\n",
    "    K = np.dot(np.dot(p_ ,H(m_).transpose()), np.linalg.inv(S))\n",
    "    y_ = np.dot(Q(m_).transpose(),np.array(g + F_p))\n",
    "    v = Y[i]  - y_;\n",
    "   # print(v)\n",
    "   # print(K)\n",
    "    v = np.dot(K , v.transpose())\n",
    "    v = v.tolist();\n",
    "    q =  norm(m_  + v)\n",
    "    m.append(q)\n",
    "#    print(m_ + v)\n",
    " #   print(p_  - np.dot(np.dot(K ,S),K.transpose()))\n",
    "    P.append(p_  - np.dot(np.dot(K ,S),K.transpose()))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "3aa9d8ca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fbbe76f9d30>]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = t\n",
    "y = [a[0] for a in X]\n",
    "fig3 = plt.figure(1)\n",
    "axes1 = fig3.subplots(1, 1)\n",
    "axes1.plot(x, [a[0] for a in X],label='parametric curve')\n",
    "axes1.plot(x, [a[0] for a in m],label='parametric curve')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "cf1b1563",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fbbe75e4490>]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = t\n",
    "fig1 = plt.figure(1)\n",
    "axes1 = fig1.subplots(1, 1)\n",
    "axes1.plot(x, [a[1] for a in X],label='parametric curve')\n",
    "axes1.plot(x, [a[1] for a in m],label='parametric curve')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "7870f983",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fbbe7559730>]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = t\n",
    "fig2 = plt.figure(1)\n",
    "axes1 = fig2.subplots(1, 1)\n",
    "axes1.plot(x, [a[2] for a in X],label='parametric curve')\n",
    "axes1.plot(x, [a[2] for a in m],label='parametric curve')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "62c34534",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fbbe74c9100>]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = t\n",
    "fig4 = plt.figure(1)\n",
    "axes1 = fig4.subplots(1, 1)\n",
    "axes1.plot(x, [a[3] for a in X],label='parametric curve')\n",
    "axes1.plot(x, [a[3] for a in m],label='parametric curve')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "dec5d84d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d925c875",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3efe8d3a",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "70094d55",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
